Problems Related to Stimulated Electromagnetic Emissions, Strong Turbulence and Ionospheric Modification
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r- 1 / 1. v <- 7 Problems Related to Stimulated Electromagnetic Emissions, Strong Turbulence and Ionospheric Modification Simon Goodman IRF Scientific Report 212 May 1993 ISSN 0284-1703 INSTITUTET FÖR RYMDFYSIK Swedish Institute of Space Physics Uppsala Division Problems Related to Stimulated Electromagnetic Emissions, Strong Turbulence and Ionospheric Modification by SIMON GOODMAN Swedish Institute of Space Physics, Uppsala Division S-75591 Uppsala, Sweden Doctoral thesis at Uppsala University IRF Scientific Report 212 May 1993 Printed in Sweden Swedish Institute of Space Physics Kiruna 1993 ISSN 0284-1703 Doctoral thesis at Uppsala University 1993 Abstract Goodman, S.. 1993, Problems Related to Stimulated Electromagnetic Emissions, Strong Turbulence and Ionospheric Modification. Swedish Institute of Space Physics. IRF Scien- tific Report 212, 95 pp. Uppsala. ISSN 0284-1703. Optical pumping of the ionospheric plasma by high-frequency radio waves produces a state of turbulence. Several consequences of the pumping are considered in this thesis. At reflection altitude the plasma is thought to be dominated by parametric instabilities and strong turbulence; these are both encapsulated in the so called Zakharov equations. The Zakharov equations are derived and generalised from kinetic theory. Limits of validity, corrections to the ion sound speed, effective ponderomotive force, nonlinear damping and other generalisations are included. As an example of the difference a kinetic approach makes, the threshold for parametric instabilities is seen to be lowered in a kinetic plasma. Mostly relevant to the upper hybrid layer is the recent discovery in the pumping ex- periments of stimulated electromagnetic emissions (SEE). In particular one feature of SEE which occurs around the cyclotron harmonics and depends on density striations is investi- gated. The observed frequency of emission, dependency on striations, time evolution and cutoff frequency below which the feature does not occur, are explained. Two theoretical approaches are taken. The first is a parametric three wave decay instability followed by a nonlinear mixing to produce SEE. Thresholds for the instability are well within exper- imental capacity. The second, less orthodox, approach, is a finite amplitude model. The finite amplitude model goes beyond the traditional parametric approach by being able to predict radiated power output. Miscellaneous aspects of a turbulent ionosphere are also examined. The dependency of the s«. rtering cross section of a turbulent plasma upon higher order perturbations is considf r / In a turbulent plasma, density gradients steeper than characteristic plasma scales -. , develop. The case of calculating the dielectric permittivity for a linear gradient of ar • <r steepness is considered. Sim i r'j )dman, Swedish Institute of Space Physics, Uppsala Division, S-755 91 Uppsala, Sw( i © Simon Goodman, 1993 ISSN 0284-1703 Printed in Sweden by Swedish Institute of Space Physics, Kiruna, 1993. CONTENTS LIST OF FIGURES Ö LIST OF TABLES 6 ACKNOWLEDGEMENTS 7 1 INTRODUCTION 9 1.1 Outline of the Thesis i2 2 BACKGROUND PLASMA PHYSICS 13 2.1 Basic Kinetic Theory 13 2.2 Linear Dispersion Relations for Electrostatic Waves 14 2.3 Damping 16 2.4 Dielectric Permittivity for a Magnetized Plasma 16 2.5 Dispersion Relation for Bernstein Waves 19 2.6 The Zakharov Equations 20 2.7 The Ionosphere 22 3 STRONG TURBULENCE EQUATIONS DERIVED FROM KINETIC THEORY 25 3.1 Introduction 25 3.2 The Low Frequency Equation 27 3.3 The High Frequency Equation 30 3.4 Conclusion 36 4 A COMBINED PARAMETRIC AND CONVERSION MECHANISM FOR UPSHIFTED STIM- ULATED ELECTROMAGNETIC EMISSIONS 38 4.1 Introduction 38 4.2 Kinematics 40 4.2.1 Case A: Both pump waves are upgoing 42 4.2.2 Case B: One pump wave is upgoing, the other is downgoing 42 4.3 Resonant Instability 42 4.4 Thresholds and Cutoff Frequency 44 4.5 Conclusion 47 5 STIMULATED ELECTROMAGNETIC EMISSIONS FROM MAGNETIZED AND INHOMO- GENEOLS PLASMA 48 5.1 Introduction 48 5.2 Calculation of Currents 50 5.3 The Pump Wave 52 5.4 Excitation ot Perpendicular Wave Modes 53 5.4.1 The Electron Bernstein Modes 53 5.4.2 Lower Hybrid Mode Excitation 56 5.5 Radiation Field 60 5.6 Conclusions 62 6 ELECTRON CYCLOTRON HARMONIC DEPENDENCE OF THE FREQUENCY CUTOFF IN STIMULATED ELECTROMAGNETIC EMISSIONS 63 6.1 Introduction 63 6.2 The theoretical model 65 6.3 Cutoff Frequency 66 6.4 Conclusion 70 7 QUESTIONS RELATING TO THE SCATTERING CROSS SECTION OF A TURBULENT IONOSPHERIC PLASMA 72 7.1 Introduction 72 7.2 Basic Non-Linear Equations 73 7.3 Periodic or Vanishing Boundary conditions 74 7.4 Estimate of Q 75 7.5 Discussion 78 7.6 Conclusion 80 8 PERMITTIVITY OF INHOMOGENEOUS AND MAGNETIZED PLASMA 81 8.1 Introduction 81 8.2 Permittivity Wave Equation 84 8.3 Conclusion 88 BIBLIOGRAPHY 91 LIST OF FIGURES 2.1 Geometry of Magnetized System 17 2.2 Electron Density in the Ionosphere and Neutral Atmosphere Temperature . 24 2 3.1 Comparison Between T/a and l/(l + 3r,/Te) 31 4.1 Broad Upshifted SEE away from the Cutoff 40 4.2 Broad Upshifted SEE near the Cutoff 41 4.3 Diagrammatic Representation of the Broad Upshifted SEE Process 42 4.4 The Broad Upshifted SEE Cutoff Frequency vs Cyclotron Harmonic Number 46 5.1 Heating Geometry for Northern Scandinavian Site 49 6.1 The Cutoff Frequency vs Harmonic Number for Parallel Pump 68 6.2 The Cutoff Frequency vs Harmonic Number for 19.3° Angle 69 6.3 The Cutoff Frequency vs Harmonic Number for Perpendicular Pump .... 70 6.4 The Cutoff Frequency vs Harmonic Number for 42° Angle 71 7.1 Schematic Heating Geometry 76 7.2 Field Strength * for the Cubic Schrodinger Equation 78 7.3 Field Strength * for thf> Quintic Schrodinger Equation with Q = 0.001 ... 79 7.4 Field Strength ty for the Quintic Schrodinger Equation with Q = 0.01 .... 79 8.1 Geometry of Inhomogeneous Magnetized Plasma 83 v LIST OF TABLES 2.1 Ionospheric, magnetospheric, laboratory and astrophysical plasma parameters 23 ACKNOWLEDGEMENTS An essentially infinite number of people have influenced this thesis in some way. Without two of them in particular though, the late Peter Christiansen and Bo Thidé, there would be no thesis. Peter was the one who persuaded me to do a PhD in the first place rather than enter into company life, designing pocket calculators, missiles, or the maximum number of fishfingers that can fit into the mimimum volume of fishfinger packet. He was always generous with time and always willing to listen to any stupid idea that might enter into my mind whilst in the vicinity of his office at Sussex University. His untimely death was a shock to all and he is sorely missed. Bo Thidé, my supervisor in Sweden, is a person I will always be indebted to. His immense patience, selfless regard for others, and ability to devote himself completely to work, whilst at the same time never losing his sense of humour or perspective is truly inspirational. In addition we share a similar philosophy towards doing physics and I value the many stimulating discussions we had. My time living, as a foreigner, in Sweden, would not have been as pleasant as it was if not for the kindness of the people there. Special thanks must go to the great automobile surgeons Harley Thomas and Bengt Holback for keeping my car alive, which, by all the laws of mechanics, not to mention those of traffic safety, ought to have died a much longer time before. Without my car I would not have been able to get to the institute on cold winter days and this thesis would have taken at least twice as long as it has already. Last but not least I would like to thank the Swedish Natural Science Research Council for financial support. CHAPTER 1 INTRODUCTION The last two decades have seen a vast collection of new and complex phenomena observed in experimental plasma physics. Ionospheric plasma physics has highlighted a wealth of these new phenomena. The origin of this avalanche of new discoveries in the ionosphere is undoubtedly the installation in the 1970's of powerful radio wave transmitters specifically designed not for commercial purposes but for the radio wave heating of the ionosphere. Originally expected only to heat the ionosphere in local hot spots the experiments revealed that our seemingly tame near-Earth ionospheric plasma is in fact capable of the most extreme nonlinear behaviour. For an overview of early work see [Fejer, 1975] and [Fejcr, 1979]. For more recent results of heating experiment results see [Stubbe et al., 1982] and [Stubbe and Kopka, 1983]. Before heating facilities existed our probing of the atmosphere and beyond had been purely passive—we simply observed rather than actively disturbed the equilibria in the sense of traditional laboratory experiments. Much of the new data has been associated with parametric instabilities and soli tons. Tentative theoretical interpretation of F-layer observations in terms cf classical turbulence, i.e., solitons and such like objects has, for example, been made by [Sheerin and Nicholson, 1982]. Their numerical solutions of Zakharov's equations [Zakharov, 1972] showed that the electric field near the reflection layer of the ionosphere could drive a modulational instability. Petviashvili showed that clusters of three dimensional solitons could form in the ionosphere in the final stages of a parametric instability [Petviashvili, 1976]. Solitons are an idealisation to reality and in general we expect 'cavitons', which simply means a density depletion associated with the ponderomotive force of a strorg electric field of a turbulent plasma. Direct evidence for the existence of cavi tons has been observed, for example, at the Arecibo Observatory [Won</ et al, 1981; Birkmayer et al., 1986; Cheung et al., 1989]. For detailed descriptions of the type of caviton they measure see these papers.